As someone with a mechanical engineering background, all these clever answers to the question (e.g. "manhole covers are round to prevent the cover falling in") are strange. Covers are round because the hole is round, and the hole is round because a cylindrical shape is sturdy and prevents collapse. That's it.
That's not "it". A square cover would not be feasible, without a tether system to fish them out of the literal shit, after they fall in from a few inch misalignment.
The hole came first. They dig a hole, then they have a need to put a cover on it. Making a circular cover to fit over a circular hole is if anything cheaper and easier than making a square cover over an inscribed circular hole, at least when working with metal.
The hole drove the design of the cover, not the other way around.
In this hypothetical, presuming you're putting the manhole (subsurface conduit/plumbing maintenance access point) in after you've already paved the road: it's because the tool you'd use to cut a hole into pavement (i.e. a concrete saw) cuts straight lines — and it's easier to make a square/rectangle out of straight lines than a circle. And sure enough, whenever you see workers hacking up the road, they generally are cutting square holes.
At the end of this process, you have a square hole in the pavement, opening to a square excavation, bottoming out at a square concrete foundation, on which has been set a round concrete cylinder, which is then surrounded out to the edge of the square hole with packed earth.
Given this, you could equally-well finish this job either:
1. by placing a square of metal to fill the entire square packed-earth space you've constructed (as when bridging a pothole with a temporary steel surface plate);
2. or by first paving over the exposed packed-earth part, and then placing a circle of metal to cover only the manhole entrance itself.
...which is why people do justifiably ask why, in practice, we seem to always favor option 2 over option 1.
A manhole is a hole for men to go in, not a near-surface utility access. Those square cut quick access holes often do have square metal covers.
The manhole opens up into a vertical tube, often with a ladder built into the wall, big enough around for a man to descend into a subsurface structure. Hence, manhole.
Manhole covers are always round because the tube they connect to is round, and that tube is round for structural reasons.
You wouldn't for multiple reasons. The fact that the tube you're covering is round is one of those reasons, and the primary one, but not all of the reasons. A round cover would still be used if the tubes were square.
A manhole cover has two purposes: people to traverse, but much more importantly, vehicles to traverse.
